arXiv subjects

Li-Chen Zhao

Publications and source records attributed to Li-Chen Zhao.

54 records · Page 3Linked to original sources

arXiv2016

Symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime

We study symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime of a single-mode fiber. Key characteristics of such multi-peak solitons, as the formation mechanism, propagation stability, and shape-changing collisions, are revealed in detail. Our results show that this multi-peak (symmetric or asymmetric) mode could be regarded as a single pulse formed by a nonlinear superposition of a periodic wave and a single-peak (W-shaped or antidark) soliton. In particular, a phase diagram for different types of nonlinear excitations on a continuous wave background including breather, rogue wave, W-shaped soliton, antidark soliton, periodic wave, and multi-peak soliton is established based on the explicit link between exact nonlinear wave solution and modulation instability analysis. Numerical simulations are performed to confirm the propagation stability of the multi-peak solitons with symmetric and asymmetric structures. Further, we unveil a remarkable shape-changing feature of asymmetric multi-peak solitons. It is interesting that these shape-changing interactions occur not only in the intraspecific collision (soliton mutual collision) but also in the interspecific interaction (soliton-breather interaction). Our results demonstrate that each multi-peak soliton exhibits the coexistence of shape change and conservation of the localized energy of light pulse against the continuous wave background.

nlin.PS↗

arXiv2015

Quantitative Relation between Modulational Instability and Several Well-known Nonlinear Excitations

We study on the relations between modulational instability and several well-known nonlinear excitations in a nonlinear fiber, such as bright soliton, nonlinear continuous wave, Akhmediev breather, Peregrine rogue wave, and Kuznetsov-Ma breather. We present a quantitative correspondence between them based on the dominant frequency and propagation constant of each perturbation on a continuous wave background. Especially, we find rogue wave comes from modulational instability under the "resonance" perturbation with continuous wave background. These results will deepen our understanding on rogue wave excitation and could be helpful for controllable nonlinear wave excitations in nonlinear fiber and other nonlinear systems.

nlin.PS↗

arXiv2015

High-order Rogue Wave solutions for the Coupled Nonlinear Schrödinger Equations-II

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrödinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the special limitation on the wave vectors. As an application, we exhibit the first, second-order rogue wave solution and the superposition of them by computer plotting. We find the distribution patterns for vector rogue waves are much more abundant than the ones for scalar rogue waves, and also different from the ones obtained with the constrain conditions on background fields. The results further enrich and deep our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

nlin.PS↗

arXiv2015

W-shaped solitons generated from a weak modulation in the Sasa-Satsuma equation

We revisit on rational solution of Sasa-Satsuma equation, which can be used to describe evolution of optical field in a nonlinear fiber with some high-order effects. We find a striking dynamical process which involves both modulational instability and modulational stability regimes, in contrast to the rogue waves and W-shaped soliton reported before which involves modulational instability and stability respectively. It is demonstrated that stable W-shaped solitons can be generated from a weak modulation signal on continuous wave background. This provides a possible way to obtain stable high-intensity pulse from low-intensity continuous wave background.

nlin.PS↗

arXiv2015

Rogue-wave solutions of a three-component coupled nonlinear Schrodinger equation

We investigate rogue-wave solutions in a three-component coupled nonlinear Schrodinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a four-petaled flower in temporal-spatial distribution, in contrast to the eye-shaped structure in one-component or two-component systems. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

nlin.PS↗

arXiv2015

Localized nonlinear waves in a two-mode nonlinear fiber

We find that diverse nonlinear waves, such as soliton, Akhmediev breather, and rogue waves (RWs), can emerge and interplay with each other in a two-mode coupled system. It provides a good platform to study interaction between different kinds of nonlinear waves. In particular, we obtain dark RWs analytically for the first time in the coupled system, and find that two RWs can appear in the temporal-spatial distribution. Possible ways to observe these nonlinear waves are discussed.

nlin.PS↗

arXiv2014

State Transition Induced by Higher-order Effects and Background Frequency

State transition between the Peregrine rogue wave and w-shaped traveling wave induced by higher-order effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is consistent with the modulation instability (MI) analysis that involves MI region and stability region in low perturbation frequency region. In particular, the link between the MI growth rate and transition characteristic analytically demonstrates that, the size characteristic of transition is positively associated with the reciprocal of zero-frequency growth rate. Further, we investigate the case for nonlinear interplay of multi-localized waves. It is interesting that the interaction of second-order waves in stability region features a line structure, rather than an elastic interaction between two w-shaped traveling waves.

nlin.PS↗

arXiv2014

Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations

We derive generalized nonlinear wave solution formula for mixed coupled nonlinear Schödinger equations (mCNLSE) by performing the unified Darboux transformation. We give the classification of the general soliton formula on the nonzero background based on the dynamical behavior. Especially, the conditions for breather, dark soliton and rogue wave solution for mCNLSE are given in detail. Moreover, we analysis the interaction between dark-dark soliton solution and breather solution. These results would be helpful for nonlinear localized wave excitations and applications in vector nonlinear systems.

nlin.SI↗

arXiv2014

Reply to "Comment on "Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations""

In the recent comment quoted in the title (arXiv:1407.7852v1), a comment is presented on our recent work which derive a generalized nonlinear wave solution formula for mixed coupled nonlinear Schödinger equations by performing the unified Darboux transformation (arXiv:1407.5194). Here we would like to reply to the comment and clarify some facts in arXiv:1407.5194.

nlin.SI↗

arXiv2013

Novel Localized Waves in a Two-mode Nonlinear Fiber with High-order Effects

We study on rational solutions on nonzero background of coupled Sasa-Satsuma equations through Darboux transformation method, which take into account third order dispersion, the term with self-frequency shift, and the term describing self-steepening corrections to the cubic nonlinearity. We find there are some new types of localized waves in the coupled system, such as dark-antidark soliton pair, W-shaped soliton, dark W-shaped soliton, and the combined localized waves of them. The results indicate that there are abundant novel localized waves in the two-mode fiber with these high-order effects, which would inspire experimental realization in the related physical systems.

nlin.PS↗

arXiv2013

The Rogue Waves with Quintic Nonlinearity and Nonlinear Dispersion effects in Nonlinear Optical Fibers

We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue wave in nonlinear fibers. We find the rogue wave with these higher order effects has identical shape with the well-known one in nonlinear Schr$\ddot{o}$dinger equation. However, the quintic nonlinear term and nonlinear dispersion effect affect the velocity of rogue wave, and the evolution of its phase.

nlin.PS↗

arXiv2013

Rational W-shaped Optical Soliton on Continuous Wave in Presence of Kerr Dispersion and Stimulated Raman Scattering

We study localized wave on continuous wave background analytically in a nonlinear fiber with higher order effects such as higher order dispersion, Kerr dispersion, and stimulated inelastic scattering. We present an exact rational W-shaped soliton solutions, whose structural properties depend on the frequency of the background field. The hump value increase with the decrease of the background frequency in the certain regime. The highest value of the W-shaped soliton can be nine times the background's, and the distribution shape is identical with the one of well-known eyes-shaped rogue wave with its maximum peak. The numerical stimulations indicate that the W-shaped soliton is stable with small perturbations.

nlin.PS↗

arXiv2013

High-order Rogue Waves in Vector Nonlinear Schrödinger Equations

We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrödinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones in single component systems. The distribution shape can be quadrilateral, triangle, and line structures through varying the proper initial excitations given by the exact analytical solutions. Moreover, six fundamental rogue wave can emerge on the distribution for second-order vector rogue wave, which is similar to the scalar third-order ones. The distribution patten for vector ones are much abundant than the ones for scalar rogue waves. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

nlin.PS↗

arXiv2013

Trajectory Characters of Rogue Waves

We present a simple representation for arbitrary-order rogue wave solution and study on the trajectories of them explicitly. We find that the global trajectories on temporal-spatial distribution all look like "X" shape for rogue waves. Short-time prediction on rogue wave can be done through measuring the information contained in the initial perturbation twice.

cond-mat.quant-gas↗

arXiv2013

Pair-Tunneling Induced Localized Waves in a Vector Nonlinear Schrödinger Equation

We investigate the localized waves of the coupled two-mode nonlinear Schrödinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov-Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal-spatial structures. The phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Our results have implications in such diverse fields as Bose-Einstein condensate, nonlinear fibers and super fluids.

nlin.PS↗

arXiv2013

Darboux transformation and multi-dark soliton for N-component coupled nonlinear Schrödinger equations

In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and multi-dark soliton solutions for multi-component coupled NLS with defocusing case and mixed focusing and defocusing case. Some exact single and two-dark solitons of three-component NLS equation are shown by plotting the picture.

nlin.SI↗

arXiv2013

Temporal-Spatial Interference Pattern During Solitons Interaction

Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference pattern is determined by the relative velocity of the solitons, and the temporal pattern behavior is determined by the peak amplitudes and the kinetic energy of the solitons. Analytical expressions for the periods of the interference patterns are obtained. A method for classifying the nonlinearity of many nonlinear systems is proposed. As an example, we discuss possibilities to observe these properties of solitons in a nonlinear planar waveguide.

nlin.PS↗

arXiv2011

Bright Chirp-free and Chirped Nonautonomous solitons under Dispersion and Nonlinearity Management

We present a series of chirp-free and chirped analytical nonautonomous soliton solutions to the generalized nonlinear Schrodinger equation (NLSE) with distributed coefficients by Darboux transformation from a trivial seed. For chirpfree nonautonomous soliton, the dispersion management term can change the motion of nonautonomous soliton and do not affect its shape at all. Especially,the classical optical soliton can be presented with variable dispersion term and nonlinearity when there is no gain. For chirped nonautonomous soliton, dispersion management can affect the shape and motion of nonautonomous solitons meanwhile. The periodic dispersion term can be used to control its "breathing" shape, and it does not affect the trajectory of nonautonomous soliton center with a certain condition.

physics.optics↗